In this thesis we use computational techniques (numerical simulations) to study different stages of black hole mergers. A first project describes topological properties of the main performer of this play, the black hole and its event horizon. We investigate three configurations: a continuum ring singularity, a 'discretized' ring (black holes arranged on a ring), and a linear distribution of black holes. We evolve each of the corresponding spacetimes forward and then backwards in time, searching for the respective event horizons.
We find some evidence, based on configurations of multiple BHs arranged in a ring, that this configuration leads to singular limit where the horizon width has zero size, possibly indicating the presence of a naked singularity, when the radius of the ring is sufficiently large. In a second project, we study the dynamics of a hydrodynamical accretion disk around a recoiling black hole, which models the behavior of an accretion disk around a binary just after the merger, using 'smoothed-particle hydrodynamics' techniques. We simulated different recoil angles between the accretion disk and the recoil velocity of the black hole.
We find that for more vertical kicks (angles < 30 degrees) a gap remains present in the inner disk, while for more oblique kicks (angles > 45 degrees), matter rapidly accretes toward the black hole. There is a systematic trend for higher potential luminosities for more oblique kick angles for a given black hole mass, disk mass and kick velocity, and we find large amplitude oscillations in time in the case of a kick oriented 60 degrees from the vertical.